B-IncStrDB

Utilizing a unified structure model in (3 + 1)-dimensional superspace to identify a homologous phase (Ga_1-αAl_α)₂O₃(ZnO)_m in ZnO-based thermoelectric composites

Authors:

Michiue, Yuichi; Son, Hyoung-Won; Mori, Takao

Journal:

Journal of Applied Crystallography 53 1542-1549 (2020)

DOI:

https://doi.org/10.1107/S1600576720013898

B-IncStrDB ID: Thi3ZYe1irN Entry date: 2022-01-20 Last revision: 2022-02-15

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sample_I_m_37_3d

Chemical data

Structural Formula Sum: Zn39 O40 [ Help ]

Formula weight: 3189.8 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Space group name (H-M): C m c m [ Help ]

Space group name (Hall): -C -2x;-2yc;-2zc [ Help ]

Space group nb.: 63 [ Help ]

Symmetry operations of the space group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x,y,z
2	-x,-y,z+1/2
3	-x,y,-z+1/2
4	x,-y,-z
5	-x,-y,-z
6	x,y,-z+1/2
7	x,-y,z+1/2
8	-x,y,z
9	x+1/2,y+1/2,z
10	-x+1/2,-y+1/2,z+1/2
11	-x+1/2,y+1/2,-z+1/2
12	x+1/2,-y+1/2,-z
13	-x+1/2,-y+1/2,-z
14	x+1/2,y+1/2,-z+1/2
15	x+1/2,-y+1/2,z+1/2
16	-x+1/2,y+1/2,z

a: 3.2573(5) Å [ Help ]

b: 19.796(3) Å [ Help ]

c: 115.99889(17) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 7479.9(17) Å³ [ Help ]

Z: 8 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 27.537 mm^-1 [ Help ]

Refinement details

R(obs): 0.0485 [ Help ]

wR(obs): 0.0512 [ Help ]

R(all): 0.0546 [ Help ]

wR(all): 0.0518 [ Help ]

S(all): 1.88 [ Help ]

Nb. of parameters: 38 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0482 [ Help ]

Δ/σ(mean): 0.0136 [ Help ]

Δρ(max): 1.12 e_Å^-3 [ Help ]

Δρ(min): -1.08 e_Å^-3 [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group
Zn1	Zn	0.194404	0.007418	Uiso	0.01	8	1	d	.	.	.
Zn2	Zn	0.816347	0.020059	Uiso	0.01	8	1	d	.	.	.
Zn3	Zn	0.438481	0.032687	Uiso	0.01	8	1	d	.	.	.
Zn4	Zn	0.06052	0.045377	Uiso	0.01	8	1	d	.	.	.
Zn5	Zn	0.68221	0.058187	Uiso	0.01	8	1	d	.	.	.
Zn6	Zn	0.303429	0.071127	Uiso	0.01	8	1	d	.	.	.
Zn7	Zn	0.924233	0.084154	Uiso	0.01	8	1	d	.	.	.
Zn8	Zn	0.544838	0.097188	Uiso	0.01	8	1	d	.	.	.
Zn9	Zn	0.165532	0.110139	Uiso	0.01	8	1	d	.	.	.
Zn10	Zn	0.786571	0.122945	Uiso	0.01	8	1	d	.	.	.
Zn11	Zn	0.408081	0.135592	Uiso	0.01	8	1	d	.	.	.
Zn12	Zn	0.030024	0.148112	Uiso	0.01	8	1	d	.	.	.
Zn13	Zn	0.652222	0.160573	Uiso	0.01	8	1	d	.	.	.
Zn14	Zn	0.274453	0.173053	Uiso	0.01	8	1	d	.	.	.
Zn15	Zn	0.896564	0.185615	Uiso	0.01	8	1	d	.	.	.
Zn16	Zn	0.51856	0.198296	Uiso	0.01	8	1	d	.	.	.
Zn17	Zn	0.140635	0.2111	Uiso	0.01	8	1	d	.	.	.
Zn18	Zn	0.763129	0.224007	Uiso	0.01	8	1	d	.	.	.
Zn19	Zn	0.386424	0.236985	Uiso	0.01	8	1	d	.	.	.
Zn20	Zn	0.572846	0.505298	Uiso	0.01	8	1	d	.	.	.
Zn21	Zn	0.951752	0.518108	Uiso	0.01	8	1	d	.	.	.
Zn22	Zn	0.330981	0.53098	Uiso	0.01	8	1	d	.	.	.
Zn23	Zn	0.710288	0.543848	Uiso	0.01	8	1	d	.	.	.
Zn24	Zn	0.089401	0.556642	Uiso	0.01	8	1	d	.	.	.
Zn25	Zn	0.468134	0.569326	Uiso	0.01	8	1	d	.	.	.
Zn26	Zn	0.846449	0.581911	Uiso	0.01	8	1	d	.	.	.
Zn27	Zn	0.224472	0.594457	Uiso	0.01	8	1	d	.	.	.
Zn28	Zn	0.60242	0.607039	Uiso	0.01	8	1	d	.	.	.
Zn29	Zn	0.980519	0.61972	Uiso	0.01	8	1	d	.	.	.
Zn30	Zn	0.358884	0.632526	Uiso	0.01	8	1	d	.	.	.
Zn31	Zn	0.737478	0.645437	Uiso	0.01	8	1	d	.	.	.
Zn32	Zn	0.116098	0.658408	Uiso	0.01	8	1	d	.	.	.
Zn33	Zn	0.494458	0.671396	Uiso	0.01	8	1	d	.	.	.
Zn34	Zn	0.872275	0.684381	Uiso	0.01	8	1	d	.	.	.
Zn35	Zn	0.249379	0.697377	Uiso	0.01	8	1	d	.	.	.
Zn36	Zn	0.625746	0.71042	Uiso	0.01	8	1	d	.	.	.
Zn37	Zn	0.001503	0.72354	Uiso	0.01	8	1	d	.	.	.
Zn38	Zn	0.376839	0.736743	Uiso	0.01	8	1	d	.	.	.
Zn39	Zn	0.77555	0.75	Uiso	0.01	4	1	d	.	.	.
Zn40	Zn	0.983639	0.25	Uiso	0.01	4	1	d	.	.	.
O1	O	0.508925	0.013508	Uiso	0.02	8	1	d	.	.	.
O2	O	0.133015	0.025369	Uiso	0.02	8	1	d	.	.	.
O3	O	0.756225	0.037282	Uiso	0.02	8	1	d	.	.	.
O4	O	0.378415	0.049367	Uiso	0.02	8	1	d	.	.	.
O5	O	0	0.061656	Uiso	0.02	8	1	d	.	.	.
O6	O	0.621901	0.074102	Uiso	0.02	8	1	d	.	.	.
O7	O	0.244244	0.086628	Uiso	0.02	8	1	d	.	.	.
O8	O	0.866815	0.099195	Uiso	0.02	8	1	d	.	.	.
O9	O	0.488951	0.111825	Uiso	0.02	8	1	d	.	.	.
O10	O	0.110212	0.124569	Uiso	0.02	8	1	d	.	.	.
O11	O	0.730837	0.137443	Uiso	0.02	8	1	d	.	.	.
O12	O	0.351653	0.150375	Uiso	0.02	8	1	d	.	.	.
O13	O	0.973471	0.163218	Uiso	0.02	8	1	d	.	.	.
O14	O	0.596415	0.175826	Uiso	0.02	8	1	d	.	.	.
O15	O	0.219736	0.188146	Uiso	0.02	8	1	d	.	.	.
O16	O	0.842326	0.200264	Uiso	0.02	8	1	d	.	.	.
O17	O	0.463597	0.212375	Uiso	0.02	8	1	d	.	.	.
O18	O	0.084085	0.224672	Uiso	0.02	8	1	d	.	.	.
O19	O	0.705289	0.23724	Uiso	0.02	8	1	d	.	.	.
O20	O	0.328799	0.25	Uiso	0.02	4	1	d	.	.	.
O21	O	0.88464	0.498448	Uiso	0.02	8	1	d	.	.	.
O22	O	0.260972	0.510603	Uiso	0.02	8	1	d	.	.	.
O23	O	0.638258	0.522966	Uiso	0.02	8	1	d	.	.	.
O24	O	0.016243	0.535459	Uiso	0.02	8	1	d	.	.	.
O25	O	0.39433	0.547977	Uiso	0.02	8	1	d	.	.	.
O26	O	0.772078	0.560449	Uiso	0.02	8	1	d	.	.	.
O27	O	0.149505	0.572873	Uiso	0.02	8	1	d	.	.	.
O28	O	0.527021	0.585292	Uiso	0.02	8	1	d	.	.	.
O29	O	0.90506	0.597746	Uiso	0.02	8	1	d	.	.	.
O30	O	0.283714	0.610232	Uiso	0.02	8	1	d	.	.	.
O31	O	0.662664	0.622708	Uiso	0.02	8	1	d	.	.	.
O32	O	0.041408	0.635134	Uiso	0.02	8	1	d	.	.	.
O33	O	0.419612	0.647515	Uiso	0.02	8	1	d	.	.	.
O34	O	0.797324	0.659923	Uiso	0.02	8	1	d	.	.	.
O35	O	0.174884	0.672456	Uiso	0.02	8	1	d	.	.	.
O36	O	0.552666	0.685185	Uiso	0.02	8	1	d	.	.	.
O37	O	0.930793	0.698103	Uiso	0.02	8	1	d	.	.	.
O38	O	0.309041	0.711128	Uiso	0.02	8	1	d	.	.	.
O39	O	0.686931	0.724153	Uiso	0.02	8	1	d	.	.	.
O40	O	0.06393	0.737108	Uiso	0.02	8	1	d	.	.	.
O41	O	0.439644	0.75	Uiso	0.02	4	1	d	.	.	.

sample_I_m_37_4d

Chemical data

Structural Formula Sum: Ga0.397 Zn1.785 O2.182 [ Help ]

Formula weight: 179.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: orthorhombic [ Help ]

Superspace group name: Cmmm(00γ)0s0 [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,-x2,x3,x4+1/2
3	-x1,x2,-x3,-x4+1/2
4	x1,-x2,-x3,-x4
5	-x1,-x2,-x3,-x4
6	x1,x2,-x3,-x4+1/2
7	x1,-x2,x3,x4+1/2
8	-x1,x2,x3,x4
9	x1+1/2,x2+1/2,x3,x4
10	-x1+1/2,-x2+1/2,x3,x4+1/2
11	-x1+1/2,x2+1/2,-x3,-x4+1/2
12	x1+1/2,-x2+1/2,-x3,-x4
13	-x1+1/2,-x2+1/2,-x3,-x4
14	x1+1/2,x2+1/2,-x3,-x4+1/2
15	x1+1/2,-x2+1/2,x3,x4+1/2
16	-x1+1/2,x2+1/2,x3,x4

a: 3.2573(5) Å [ Help ]

b: 19.796(3) Å [ Help ]

c: 1.48716(17) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Volume: 95.90(2) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.000000	0.000000	0.012821

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2-nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	2.0
0.0	0.0	0.0	1.0

Z: 1 [ Help ]

Cell measurement temperature: 293 K [ Help ]

μ: 15.376 mm^-1 [ Help ]

Refinement details

R(obs): 0.0485 [ Help ]

wR(obs): 0.0512 [ Help ]

R(all): 0.0546 [ Help ]

wR(all): 0.0518 [ Help ]

S(all): 1.88 [ Help ]

Nb. of parameters: 38 [ Help ]

Number of restraints: 0 [ Help ]

Number of constraints: 2 [ Help ]

Weighting scheme: sigma [ Help ]

Δ/σ(max): 0.0482 [ Help ]

Δ/σ(mean): 0.0136 [ Help ]

Δρ(max): 1.12 e_Å^-3 [ Help ]

Δρ(min): -1.08 e_Å^-3 [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	Atom symbol	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group	Subsystem
M1	Zn	0.3841(5)	0	Uiso	0.01	8	0.5	d	.	.	.	1
M1a	Zn	0.776(6)	0	Uiso	0.01	4	0.0128	d	.	.	.	1
M1c	Zn	-0.016(6)	0	Uiso	0.01	4	0.0128	d	.	.	.	1
O1	O	0.886(3)	0.5	Uiso	0.02	8	0.5	d	.	.	.	2

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]

Wave vector code	q_1
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	10
11	11
12	12

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
M1a	0.75	0.0128
M1c	0.25	0.0128

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
M1x1	M1	x	1
M1y1	M1	y	1
M1z1	M1	z	1
M1x2	M1	x	2
M1y2	M1	y	2
M1z2	M1	z	2
M1x3	M1	x	3
M1y3	M1	y	3
M1z3	M1	z	3
M1x4	M1	x	4
M1y4	M1	y	4
M1z4	M1	z	4
M1x5	M1	x	5
M1y5	M1	y	5
M1z5	M1	z	5
M1x6	M1	x	6
M1y6	M1	y	6
M1z6	M1	z	6
M1x7	M1	x	7
M1y7	M1	y	7
M1z7	M1	z	7
M1x8	M1	x	8
M1y8	M1	y	8
M1z8	M1	z	8
M1x9	M1	x	9
M1y9	M1	y	9
M1z9	M1	z	9
M1x10	M1	x	10
M1y10	M1	y	10
M1z10	M1	z	10
O1x1	O1	x	1
O1y1	O1	y	1
O1z1	O1	z	1
O1x2	O1	x	2
O1y2	O1	y	2
O1z2	O1	z	2
O1x3	O1	x	3
O1y3	O1	y	3
O1z3	O1	z	3
O1x4	O1	x	4
O1y4	O1	y	4
O1z4	O1	z	4
O1x5	O1	x	5
O1y5	O1	y	5
O1z5	O1	z	5
O1x6	O1	x	6
O1y6	O1	y	6
O1z6	O1	z	6
O1x7	O1	x	7
O1y7	O1	y	7
O1z7	O1	z	7
O1x8	O1	x	8
O1y8	O1	y	8
O1z8	O1	z	8
O1x9	O1	x	9
O1y9	O1	y	9
O1z9	O1	z	9
O1x10	O1	x	10
O1y10	O1	y	10
O1z10	O1	z	10
O1x11	O1	x	11
O1y11	O1	y	11
O1z11	O1	z	11
O1x12	O1	x	12
O1y12	O1	y	12
O1z12	O1	z	12

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
M1x1	0	0
M1y1	0	-0.0538(5)
M1z1	0.1031	0
M1x2	0	0
M1y2	0.0011	0
M1z2	0	-0.0515
M1x3	0	0
M1y3	0	0.0036
M1z3	-0.0328	0
M1x4	0	0
M1y4	-0.0005	0
M1z4	0	0.0242
M1x5	0	0
M1y5	0	-0.0004
M1z5	-0.014	0
M1x6	0	0
M1y6	0	0
M1z6	0	-0.0151
M1x7	0	0
M1y7	0	0.0003
M1z7	0.0161	0
M1x8	0	0
M1y8	-0.0011	0
M1z8	0	0.0011
M1x9	0	0
M1y9	0	0
M1z9	0.0111	0
M1x10	0	0
M1y10	0	0
M1z10	0	-0.0014
O1x1	0	0
O1y1	0	-0.0444(17)
O1z1	0.1023	0
O1x2	0	0
O1y2	0.0001	0
O1z2	0	-0.119
O1x3	0	0
O1y3	0	0.0074
O1z3	-0.0408	0
O1x4	0	0
O1y4	-0.0004	0
O1z4	0	-0.0245
O1x5	0	0
O1y5	0	-0.0007
O1z5	0.0362	0
O1x6	0	0
O1y6	0	0
O1z6	0	-0.0166
O1x7	0	0
O1y7	0	0.0012
O1z7	0.0201	0
O1x8	0	0
O1y8	-0.0004	0
O1z8	0	0.0048
O1x9	0	0
O1y9	0	-0.0007
O1z9	-0.0077	0
O1x10	0	0
O1y10	0.0001	0
O1z10	0	-0.0065
O1x11	0	0
O1y11	0	0.0011
O1z11	0.014	0
O1x12	0	0
O1y12	-0.0006	0
O1z12	0	0

Displacive sawtooth coefficients: (Show/hide table) [ Help ]

Atom site label	Ax	Ay	Az	Center (x0)	Width
M1	0	-7.125	0	0	0.4872
O1	0	-7.5	0	0	0.5

Utilizing a unified structure model in (3 + 1)-dimensional superspace to identify a homologous phase (Ga1-αAlα)2O3(ZnO)m in ZnO-based thermoelectric composites

Michiue, Yuichi; Son, Hyoung-Won; Mori, Takao

Journal of Applied Crystallography 53 1542-1549 (2020)

https://doi.org/10.1107/S1600576720013898

Download CIF

Open in JSmol

sample_I_m_37_3d

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

sample_I_m_37_4d

Chemical data

Crystallographic data and experimental details

Refinement details

Structural Information

Utilizing a unified structure model in (3 + 1)-dimensional superspace to identify a homologous phase (Ga_1-αAl_α)₂O₃(ZnO)_m in ZnO-based thermoelectric composites